Related papers: Conserved quantities in General Relativity: the ca…
We establish the charged Penrose inequality for time symmetric initial data sets having an outermost minimal surface boundary and finitely many asymptotically cylindrical ends, with an appropriate rigidity statement. This is accomplished by…
We prove the existence of a large class of initial data for the vacuum Einstein equations which possess a finite number of asymptotically Euclidean and asymptotically conformally cylindrical or periodic ends. Aside from being asymptotically…
We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy…
A spherically symmetric spacetime is presented with an initial data set that is asymptotically flat, satisfies the dominant energy condition, and such that on this initial data $M<\sqrt{A/16\pi}$, where M is the total (ADM) mass and A is…
In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and with nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and Witten, we prove the following theorem: For…
We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities
We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal.…
We summarize results on the Penrose inequality bounding the ADM-mass or the Bondi mass in terms of the area of an outermost apparent horizon for asymptotically flat initial data of Einstein's equations. We first recall the proof, due to…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry…
Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over…
Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in…
According to the classical Penrose inequality, the mass at spatial infinity is bounded from below by a function of the area of certain trapped surfaces. We exhibit quantum field theory states that violate this relation at the semiclassical…
In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -6 and negative mass when the genus of the conformal boundary at infinity is positive. Using inverse mean curvature flow, we…
The classical view of mass is that it quantifies the amount of substance and is a kinematical parameter. All matter has an attribute of mass and is a conserved quantity in any interaction. With the advent of special relativity, mass became…
The notions of "motion" and "conserved quantities", if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity,…
Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a…